How can one machine ping another, but the reverse ping doesn't work

Solution 1:

I think what Barlop says in comments is the most likely cause.

Your question asked why this is happening... When you connect to a network, Windows asks you to select a location - public, home or office.

Each profile has different default firewall walls, although I don't remember them blocking ping by default other than on Windows Server (but, I am probably wrong - been a while since I last looked).

That being said, all of these settings can be overwritten by group policy, so, a network administrator may have chosen to lock down the machine.

In any way, unless this is enforced/made so that you can not overwrite it, it is pretty trivial to change.

-edited this section -

The default domain profile does block ping by default...

Click on the Start Orb and type "Windows Firewall" (or as much as needed) and then when it comes up in the results, click on Windows Firewall with Advanced Security. From here, click on Inbound Rules and look for File and Printer Sharing (Echo Request - ICMPv4-In) and simply enable it...

... but, it should be enabled already for the private and public profiles... Look for the one above it that says "Domain" in the profile column and simply click enable in the action bar on the right.